He vertices of a triangle are p(-3,8), q(-6,-4), and r(1,1). name the vertices of the image reflected in the x-axis

P'(-3, -8), Q'(-6, 4), R'(1, -1)

Step-by-step explanation:

When you reflect a point (x, y) across the x-axis, the x-coordinate remains the same, but the y-coordinate gets the opposite sign: it becomes (x, -y).

Thus, if a point P, say, (-3, 8) is eightn units above the x-axis, its reflection P' will be the same distance below, at (-3, -8).

Thus, we get the following transformations.

P (-3, 8)   ⟶ P' (-3, -8)

Q (-6, -4) ⟶ Q' (-6, 4)

R (1, 1)      ⟶ R' (1, -1)

Thus, the vertices of the reflected triangle are P' (-3, -8), Q' (-6, 4), R' (1, -1).

The image below shows ∆PQR and its reflection ∆P'Q'R' across the x-axis.

Angle E = 180 -45 -63 = 72 degrees
Using the Law of Sines
FD / sine (E) = ED / sine (63)
3.8 / 0.95106 = ED / 0.89101
side DE = 3.8 * .89101 / .95106
side DE = 3.5600677139

Source:
http://www.1728.org/trigtut2.htm